Generating of fusion plasma neutron source
with AFSI for Serpent MC neutronics
computing Serpent UGM 2015 Knoxville, TN, 14.10.2015
Paula Sirén
VTT Technical Research Centre of Finland, P.O Box 1000, 02044 VTT, Finland
1/15
20/10/2015
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Outline
Introduction to magnetically confined fusion
• Reactions
• General features in the modelling of neutron source in toroidal geometry
Neutron production in a plasma
• Codes & code systems
Tools
• Data structure
• Example cases
Serpent neutron source
• Remarks
• Questions?
Conclusions, further studies & open questions
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Tokamak concept & geometry
R
Z
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Computational fusion neutron source - generally
Neutron production rate per reaction
𝐷 + 𝐷 → 𝐻𝑒3 + 𝑛 + 3.27𝑀𝑒𝑉
𝐷 + 𝑇 → 𝐻𝑒4 + 𝑛 + 17.60𝑀𝑒𝑉
Different reaction types
• Thermal DD
• Thermal DT (main plasma, ~1-10 keV)
• Fast DD (RF heated and NBI particles
~100 keV-1 MeV)
• Fast DT
• Thermal-Fast DD
• Thermal-Fast DT
• Fast-Thermal DT
Neutron is
defined: • Location
• Energy
• Direction
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Connection between plasma physics and neutronics E
xp
eri
men
tal
data
• T
• n
• Plasma geometry (𝜓, 𝐹, 𝜌)
• NBI system geometry
• Tokamak wall geometry
Co
mp
uta
tio
nal
fusio
n r
eacti
on
rate
s
• Neutron production rates in different reaction types
• AFSI [1], ASCOT [2,3]
• JINTRAC [4]
Ne
utr
on
so
urc
e
• Source neutrons
• x, y, z
• E
• 𝜑
[1] S. Äkäslompolo, O. Asunta, P. Sirén: AFSI Fusion Source Integrator for tokamak fusion reactivity calculations. Under
preparation.
[2] J. A. Heikkinen et al. 2001 J. Comput. Phys. 173 527-548.
[3] E.Hirvijoki et al. 2014 Computer Physics Communications 185 1310–1321
[4] S. Wiesen et al. 2008. JET-ITC Report
Serpent
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Modelling in tokamak geometry
1.
Approximation
1D (or 1.5D)
Radial distribution 𝝆
2. Approximation
Poloidal cross section (𝜌𝜃 or Rz)
Full 3D toroidal geometry
𝜌𝜃, 𝜑 or 𝑅𝑧, 𝜑
Thermal particle reactions
T, n, p constant on the magnetic flux
surfaces
If localised distribution is
needed (fast particles)
Fluid codes
Usually symmetry can be utilised
Plasma is toroidally
symmetric, chamber not!
Level of
neutron
source
model
Averaging over flux
surfaces if needed by
different coupled codes
Major part of neutrons will be produced
in thermal particle reactions in ITER-size
tokamaks!
Kinetic codes
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Generating of the neutron source - tools
ASCOT (Accelerated Simulation of Charged particle Orbits in Tori)
J. A. Heikkinen et al. 2001 J. Comput. Phys. 173 527-548.
E. Hirvijoki et al. 2014 Computer Physics Communications 185 1310–1321
Fast (minority) particle orbit-following MC code
Developed 1990- at VTT and Aalto University
Powerful and widely used in the analysis (fusion alphas, beam particles) of several fusion devices
Coupled to JINTRAC [1] and ETS [2] code package
Generating a test particle ensemble
Orbit following of test particle by using MC collision operator
𝜕𝑓
𝜕𝑡= 𝒙 ∙
𝜕𝑓
𝜕𝒙+ 𝒗 ∙
𝜕𝑓
𝜕𝒗=
𝜕𝑓
𝜕𝑡𝑐𝑜𝑙𝑙
Solving Fokker-Planck
equation (distribution function)
with test particle ensemble
f(v, x), v(x)
[1] S. Wiesen et al. 2008. JET-ITC Report.
[2] D. P. Coster et al. 2010. E IEEE Transactions on plasma
science 38 9.
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AFSI-ASCOT connection
– computing of neutron production rates
ASCOT4
Input:
T, n, geometry/equilibrium
Output:
Fast particle distributions 𝑓𝐵 , 𝑣𝐵 , (beam current density, power depositions…)
AFSI Fusion Source Integrator for tokamak fusion reactivity calculations
Input:
T, n, geometry/equilibrium, fast particle distributions 𝑓𝐵, 𝑣𝐵
Output:
Neutron (or alpha particle) production rates
𝑹𝒊𝒋 in different reaction types
𝑬𝒏
Example: Fast-thermal (beam-thermal) particle reaction
𝑹𝑩𝑻 = 𝑓𝑇(𝑣𝑇)( 𝑣𝐵 − 𝑣𝑇 )𝑓𝐵(𝑣𝐵)( 𝑣𝐵𝑣𝐵𝑣𝑇
− 𝑣𝑇 ) 𝑑𝑣𝑇𝑑𝑣𝐵
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AFSI - Further development steps
Neutron production rate and energy distribution
in 2D for different reaction types
Thermal particle
reactions
DD, DT
Beam particle
reactions
DD, (DT)
RF heated particles
reactions
ASCOT RF module
Connection to some
coupled code
system
DEMO, ITER: ETS
JET: JINTRAC
Connection to
some coupled
code system
Connection to
some coupled
code system
Input data
Input data
Input data
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Neutron source - geometrical distribution 1/2
𝝆𝜽 grid
Radial position (normalised radial
coordinate) 𝝆
Poloidal angle 𝜽
Simple to scale geometrical features
(R, a, ellipticity, triangularity, inverse
aspect ratio…)
of source plasma
• Sensitivity tests
• ITER/DEMO prospects
• Fluid code input 𝜌 -> 1D
approximation
Rz grid
Position in Rz matrix
Better accuracy of local
distribution
(fast particle reactions &
energy distribution!)
2D distribution
(poloidal cross section)
Both of these will be implemented to the
neutron source model!
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Geometrical distribution 2/2
• Radial position (normalised
radial coordinate) 𝝆
• Poloidal angle 𝜽
• Toroidal angle 𝝋 Example case: Neutron production in thermal DT
reactions in ITER baseline Q=10 plasma with D/T mix
(50%/50%) computed by AFSI
3D distribution
Z
or R, z
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Neutron source practically:
Defining of probability distributions
1. Probability of reaction DD: 20.44%,
DT: 79.56%
2. Probability of radial position
𝑃𝐷𝐷 𝜌 =𝑛 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝑖𝑛 𝐷𝐷 𝑎𝑡𝜌
𝑡𝑜𝑡𝑎𝑙 𝑛 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝑖𝑛 𝐷𝐷
𝑃𝐷𝑇(𝜌) = ⋯ 3. Probability of location in the poloidal
flux surfaces isotropic
4. Probability of toroidal angle isotropic
5. Probability of energy discrete DD:
2.45 MeV, DT: 14.08 MeV
Example cases:
JET (DT 70/30) #42976 t = 12.3 s (thermal particle reactions)
ITER (DT 50/50) baseline Q=10 (thermal particle reactions)
1. Probability of reaction DD: 0.3%, DT:
99.7%
2. Probability in Rz grid
𝑃𝐷𝐷 𝑅𝑧𝑖 =𝑛 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝑖𝑛 𝐷𝐷
𝑡𝑜𝑡𝑎𝑙 𝑛 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝑖𝑛 𝐷𝐷
𝑃𝐷𝑇(𝑅𝑧𝑖) = ⋯
3. Probability of toroidal angle isotropic
4. Probability of energy discrete DD:
2.45 MeV, DT: 14.08 MeV
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Serpent neutron source data structure
General data
Reaction (1) data
Geometrical data
Reaction (2) data
Reaction (n) data
.
.
.
• Probability per reaction
• Time
• Energy (size of grid, values,
probability distribution)
• Link to geometrical data
Geometrical distribution
(size of grid, grid,
probability distribution)
𝜌𝜃𝜑 grid or
Rz𝜑 grid
• Magnetic axis
• Plasma
boundary
coordinates
• Coordinate
system
• Number of
reactions
• Number of
time points
• Link to
reaction data
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Plasma related effects in modelling which could affect neutronics results
D/T mix
DT
𝑝, 𝑛, 𝑇 Heating (NBI)
system
(beam
alignment,
power ->
Fast particle
distributions)
Plasma
geometry
(D-shape
model vs.
Grad-
Shafranov
solver)
Temperature,
density profiles
(total neutron
production,
production peaked
to the centre,
interaction with fast
particles…)
Mix of fuel
(Ratio of 2.45
MeV and
14.08 MeV
neutrons)
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Time-dependent neutron source
Example case: time-independent neutron source
Data profiles (n, T) from one time point are used
Good approximation in flat-top phase for baseline plasmas
In time-dependent simulations, probabality distributions
should be updated
Source is strongly peaked near the magnetic axis in
advanced tokamak plasmas
effect on the neutron energy distribution and the total amount of
produced neutrons
Routines to use time-dependent source are available in Serpent (if
data is available)!
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Conclusions, challenges & Open questions
Collaboration in the developing of neutron source model is very limited. (Collaboration with CCFE neutronics
is existing but not in plasma physics-neutronics coupling).
Model validation
Serpent calculations with fusion plasma neutron source will be validated with the data from existing device
(Work under JET DT campaingn?).
What is the real role of the modelling of plasma physics and neutron source in the complete analysis of
neutronics? How important is it practically (heat deposition, material damage, activation etc)?
Current status of neutron source:
ITER 15 MA NBI-heated DT plasma
Distribution of neutrons produced by thermal particle reactions is defined based on AFSI -
ASCOT simulations
Realistic fast particle reaction distributions will be inplemented to AFSI in the next
phase
JET DT record shots #42976, #42974
Neutron source calculated by JINTRAC-ASCOT(AFSI) simulations
Neutrons from thermal and beam particle reactions included
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